The quantum kinetic evolution of neutrinos in dense environments, such as the core-collapse supernovae or the neutron star mergers, can result in fast flavor conversion (FFC), presenting a significant challenge to achieving robust astrophysical modeling of these systems. Recent works that directly simulate the quantum kinetic transport of neutrinos in localized domains have suggested that the asymptotic outcome of FFCs can be modeled by simple analytical prescriptions when coarse grained over a size much larger than the FFC length scale. In this Letter, by leveraging such a scale separation, we incorporate the analytical prescriptions into global simulations that solve the classical neutrino transport equation including collisions and advection under spherical symmetry. We demonstrate that taking this approach allows to obtain results that quantitatively agree with those directly from the corresponding global quantum kinetic simulations and precisely capture the collisional feedback effect for cases where the FFC happens inside the neutrinosphere. Notably, the effective scheme does not require resolving the FFC time and length scales, hence only adds negligible computational overhead to classical transport. Our work highlights that efficient and robust integration of FFCs in classical neutrino transport used in astrophysical simulation can be feasible.